If \(X\)  is positive semidefinite, we write \(X\ge 0\) .
For two Hermitian matrices \(A\)  and \(B\)  with the same order,
\(A\ge B\)  means \(A-B\ge 0\) .
It is easy to verify that \(\ge \)  is a partial ordering on the set of Hermitian matrices,
referred to Löwner ordering.
If \(A=\Bigl [ {\begin{matrix}A_{11} & A_{12} \\ A_{21} & A_{22} \end{matrix}}\Bigr ]\) 
is a square matrix with \(A_{11}\)  nonsingular, then the Schur complement of \(A_{11}\)  in \(A\) 
is defined as \(A/A_{11}:=A_{22}-A_{21}A_{11}^{-1}A_{12}\) .
It is obvious that \(\det (A/A_{11})=(\det A)/(\det A_{11})\) .
We refer to the integrated survey [1]} for more applications of Schur complement.
